Rewrite as a simplified fraction. ${1.\overline{7} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}10x &= 17.7777...\\ 1x &= 1.7777...\end{align*}}$ Subtracting the two equations, we have: ${9x = 16}$ ${x = \dfrac{16}{9}} \text{or} {1 \dfrac{7}{9}}$